Kawahara-Burgers equation on a strip

TL;DR

This paper studies the Kawahara-Burgers equation on a strip, proving existence, uniqueness, and exponential decay of solutions without restrictions on the strip's width, in both regular and weak solution frameworks.

Contribution

It establishes the existence, uniqueness, and decay properties of solutions to the 2D Kawahara-Burgers equation on a strip, extending previous results to unbounded domains.

Findings

Existence and uniqueness of regular and weak solutions.

Exponential decay of small solutions.

Results hold without restrictions on strip width.

Abstract

An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in the $L^2$-norm.